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lfunc_lfunctions • Show schema
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{'Lhash': '1614565765690072868367523811140', 'a10': [1.8481625127765828, 5.833929369859419e-62], 'a2': [-0.3888661880650398, 0.6735359950742832], 'a3': [0.0, 0.0], 'a4': [0.6975661755595302, 1.2082200577106175], 'a5': [-1.188173830420214, -2.0579774425115382], 'a6': [0.0, 0.0], 'a7': [1.2506881961521843, -2.1662555001622534], 'a8': [-2.6405043507119306, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.487', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1146687549347843233765471787471', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.3888661880650398, -0.6735359950742832], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.188173830420214, 2.0579774425115382], [-2.5, 4.330127018922194]], [[1.0, 0], [-1.2506881961521843, 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'prelabel': '2-3e6-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -5.364538986652599e-61, 'root_number': '1.0 - 1.6853196270363839e-60*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.000000000000000000000000000000000000000000000000000000000000268226949333', 'prec': 250}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27366781146112692728748362775', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.79088006352780943250900595982', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37238969029074383001250513887', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '9.7', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/c/d/487/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-3e6-9.7-c1-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3e6-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -2.6822694933262994e-61, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27366781146112692728748362775', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1614565765690072868367523811140', 'Lhash_array': ['1614565765690072868367523811140'], 'label': '2-3e6-9.7-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/c/d/487/2'}